Modeling the magnetic interactions between paramagnetic particles helps to describe the mechanical properties of magnetorheological fluids and enables microstructure simulation. Traditional simplified models exhibit limitation of insufficient accuracy in the near-field. To address this issue, we established a new simplified model based on magnetic dipoles, analogous to solving electric field problems with electric dipoles. Compared with traditional simplified models, the proposed model incorporates higher-order terms of the induced magnetic field. Numerical simulations demonstrate that this model effectively improve the calculation accuracy of magnetic forces along the magnetic field direction for end particles. This advancement makes it a promising approach for calculating the magnetic pressure on particles, thereby facilitating the description of frictional forces between particles.